Cationic polymers obtained by cationic polymerization of branched alpha-olefins such as 4-methyl-1-pentene have been long known. For example, Japanese Patent Publn. No. 24480/1965 describes a process for polymerizing 3-methyl-1-butene or 4-methyl-1-pentene at low temperatures and suggests that the resulting crystalline polymers are suitable for producing plastics films or sheets. Said Japanese Patent Publn. describes that when an alpha-isomonoolefin is polymerized in the presence of a Friedel-Crafts type catalyst at a temperature of from -10.degree. C. to 100.degree. C., amorphous polymers are obtained and that the amorphous polymers are suitable for use as paints, varnish lacquers, other additives, plasticizers, reinforcing agents and diluents. Further, U.S. Pat. No. 3,299,022 describes homopolymers of branched alpha-olefins and copolymers thereof, and discloses that polymers having molecular weights of from 1,500,000 to 2,000,000 are amorphous viscoelastic solids. Furthermore, U.S. Pat. No. 3,317,501 describes cationic polymers of 4-methyl-1-pentene and discloses that polymers having molecular weights of no more than 5,000, which are obtained by polymerizing 4-methyl-1-pentene in the presence of an AlCl.sub.3 catalyst at a temperature of from 54.degree. to 170.degree. F., are tacky oils. Moreover, this patent describes that when the polymers having elasticity are mixed with polypropylene, the low-temperature impact resistance of the resulting polypropylene is improved. Further, Macromolecules, Vol, 10, No. 1 pp. 188 discloses that cationic polymers of 4-methyl-1-pentene have five structures.
We have carried out studies with respect to cationic polymers of branched alpha-olefins such as 4-methyl-1-pentene having specific properties, and have now found that these polymers are excellent as a tackifier for an adhesive which is not described in the literatures described above.